To determine the value of the function [tex]\( f(x) = 2x^2 + 1 \)[/tex] when [tex]\( x = 3 \)[/tex], we will follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(3) = 2(3)^2 + 1
\][/tex]
2. Calculate the value inside the parentheses first:
[tex]\[
3^2 = 9
\][/tex]
3. Multiply the result by 2:
[tex]\[
2 \times 9 = 18
\][/tex]
4. Add 1 to the result:
[tex]\[
18 + 1 = 19
\][/tex]
So, [tex]\( f(3) = 19 \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{19} \)[/tex].
